Permainan Catur Inggris Berbasis Android Menggunakan Algoritma Minimax. Deni Fajar Pratama • Elizabeth Nurmiyati Tamatjita • Dwi Nugraheny. Aplikasi Permainan Capsah Banting dengan Penerapan Algoritma Minimax. Hapnes Toba • Billy Kurniawan. Journal article Jurnal Teknik Informatika dan. In this lesson, we’ll explore a popular algorithm called minimax. We’ll also learn some of its friendly neighborhood add-on features like heuristic.
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Using these techniques, we can create a more flexible and powerful game playing agent. In my previous post How To Win Sudokuwe learned how to teach computers to solve the puzzle Sudoku. But that was really just a way to get our feet wet, before diving into more sophisticated methods of game playing agents. Especially those methods that can make strategic moves against an opponent! Isolation or Isola is a turn-based strategy board game where two players algoditma to confine their opponent on a 7×7 checker-like board.
Eventually, they can no longer make a move thus isolating them. There are three conditions under which the pieces can be moved —. In the above picture, you can see from the black algogitma that both players have placed their pieces on various parts of the board.
But as the game progressed, it shows that the yellow player still has three possible moves. Up and to the right, right algorutma square, and right two squares. But the blue player is out of options. Hence, the yellow player is the winner here. Yet, there is still an enormous amount of possible moves either player can make at any point during the game.
But there is no answer when it comes to strategy games. This requires strategy and some thought into how the game may turn out as it rolls along. Such games can evolve and produce an absurd amount of possible outcomes. So we need to think of how we can choose the best possible move, without spending the amount of time it took for cats to populate the Earth. Together with these, we can build a competitive AI agent.
The minimax algorithm is very popular for teaching AI agents how to play turn-based strategy games. The reason being is that it takes into account all the possible moves that players can take at any given time during the game. Miniimax, similar to how an AI agent would play a game like Sudoku, we can model the next possible moves either player can make via a search tree.
The reason being is that there are a variable number of moves each player can make at any given time during the game.
The tree shown above represents the next moves available during a game of Isolation. It has a 2×3 grid, with the bottom right square being unreachable. As you can see, the two players are a blue circle and a red cross. The top of the tree the root node illustrates a move made by the red player. The middle level illustrates the next possible moves by the blue player.
Aplikasi Permainan Tic-Tac-Toe Dengan Menggunakan Algoritma Minimax – CORE Reader
And the third level illustrates the possible moves by the red player, given wlgoritma previous move made by the blue player. Now you might be wondering, what the heck are those triangles below each move? This means minimax must traverse to the very bottom of the tree for every possible series of moves. Next, it has to assign some score e. This way, each game state or node in the tree has information about which player has the most to gain from any potential move.
In this picture, we can make a couple of observations. First minimax assigns a number to the final game outcomes at the leaf nodes. Then it propagates them upward through the tree, performing minimizations and maximizations on the way. The second level after the root node shows the next possible moves for the blue player our AI agent.
Our agent wants to maximize the available scores during its turn. So it would choose the move represented in the right-most node following the root node. In the world of strategy games, a heuristic score is essentially a subjective value we assign to some game state. This value is based on our understanding of how the game is won and lost. One idea could be to count all the next possible moves each player has at any given time, since more possible moves mean less chance of being isolated.
Another idea could be to use the value obtained from OMS and subtracting the number of next possible moves the opponent has. The above figure shows the win rates over many simulated isolation games played between AI agents using different heuristic scores. Now you can see how different our scores did during actual game play.
But there were some heuristic scores that outperformed the ones we came up with. Interestingly, the top two are almost exactly the same as improved score. The top two scores apply a factor of two and three to the value you subtract with the number of moves available to the opponent when computing the improved score.
But what if we come up with a heuristic score that takes a lot of time to compute?
What if the tree is huge? Will our AI agent have enough time to find its next best moves, while still being responsive enough during game play? But unfortunately, when playing Isolation our tree will be massive. It would take more time to search the tree and compute these values than there are years since the big bang!
By using this method, we can cut the compute and search time down to a maximum time of our choosing. This way our AI agent can respond at least as fast as a human could. It allows minimax to move level by level and compute heuristic scores until a certain time limit. Once this time limit is reached, the AI agent is forced to use the best move it discovered while having moved deeper and deeper down the tree.
Now this provides some insight into how difficult it can be. Creating an AI agent that is smart and responsive enough for strategy games, can be quite tricky, even for AI wizards. Especially if such games contain a world of possibilities. This is a well-known phenomenon called the horizon effect.
But we still need to look at arguably the most effective time slashing algorithm used when searching trees. I mean, seriously, a raisin blues group? You might have already guessed alpha-beta pruning has nothing to do with prunes, and more about reducing the size pruning algiritma our search tree.
We need to give minimax the ability to stop searching a particular region of the tree when it finds the guaranteed minimum or maximum of that particular level. How does alpha-beta pruning work? The minimax algorithm moves through the tree using depth-first search. Meaning it traverses through the tree going from left to right, and always going the deepest it can go.
It then discovers values that must be assigned to nodes directly above it, without ever looking at other branches of the tree. Alpha-beta pruning allows minimax to make just as good of decisions as minimax could do ninimax, but with a higher level of performance.
Bug di Algoritma Minimax untuk Tic Tac Toe |
Consider the following image, in which we have a tree with various scores assigned to each node. At the bottom left of the tree, minimax looks at the values 5 and 6 minimaz the bottom max level. It determines that 5 must be assigned to the min level right algogitma it. But, after looking at 7 and 4 of the right max level branch, it realizes that the above min level node must be assigned a maximum value of 4. Below is the algorithmic representation of minimax with alpha-beta pruning.
This way, alpha-beta pruning allows minimax to make good decisions that minimax could do alone, but with a higher level of performance. By using the minmax algorithm, we saw how the AI agent can mniimax the game and can make decisions based on a heuristic score. We also learned how to determine a well-defined heuristic for our given task Isolation. But we also discovered that it would be far too computationally intense to let minimax run wild.
So we had to use techniques like iterative deepening and alpha-beta pruning. These would force our AI agent to come up with the next move within a reasonable amount of time. But what if we want our AI agent to have a higher win rate while at least being as responsive as a algoritms We could even minmiax up with a heuristic score better tailored for playing Isolation.
There are also reflective properties related to the possible moves on the Isolation board.
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These become evident when we analyze the fully populated search tree, which would allow us minikax potentially slash a lot of branches algoritmma the search tree. If you want to get into the nitty-gritty details of how to implement this yourself, take a look at the code I wrote to solve this problem for my Udacity Artificial Intelligence Nanodegree.
You can find it on my GitHub repo. Follow me on Twitter and connect with me on LinkedIn! This article was originally posted on my blog. Sign in Get started. Home dev Learn to code for free. Never miss a story from freeCodeCamp. Get updates Get updates.
